Hmmm 2,000 meters sounds good.
MG 08/15 - range 2000 meters effective, 3500 meters maximum. 8mm. At 40 pounds, it would need to shed a little weight to get town to the M240B’s roughly 28 pounds. Swapping out the wood for lightweight composite would be a good start. Or modifying it to air cooling would easily meet the weight (see the 08/19.
So it sounds what they are looking for was readily available 100 years ago.
2,000 meters rules out 5.56 and 7.62.
.408 Cheytac or .416 Barret maybe.
L